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给定一个三角形，找出自顶向下的最小路径和。每一步只能移动到下一行中相邻的结点上。
例如，给定三角形：
[     [2],    [3,4],   [6,,"> 
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        <h1 class="title">leetcode120. 三角形最小路径和</h1>
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            <span>四月 11, 2020</span>
            

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            <h1 id="leetcode120-三角形最小路径和"><a href="#leetcode120-三角形最小路径和" class="headerlink" title="leetcode120. 三角形最小路径和"></a>leetcode120. 三角形最小路径和</h1><hr>
<p>给定一个三角形，找出自顶向下的最小路径和。每一步只能移动到下一行中相邻的结点上。</p>
<p>例如，给定三角形：</p>
<p>[<br>     [2],<br>    [3,4],<br>   [6,5,7],<br>  [4,1,8,3]<br>]<br>自顶向下的最小路径和为 11（即，2 + 3 + 5 + 1 = 11）。</p>
<p>和64题最小路径的解法基本一样，点(i,j)只能由(i,j-1)和(i-1,j-1)到达，也就是正上方和左上方。只不过最后并没有限定要到达最后一行的哪个点，所以最后还需要遍历一遍最后一行，找出最小的。（后面会优化）</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">minimumTotal</span><span class="params">(List&lt;List&lt;Integer&gt;&gt; triangle)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">1</span>; i &lt; triangle.size(); i ++) &#123;</span><br><span class="line">            List&lt;Integer&gt; preList = triangle.get(i - <span class="number">1</span>);<span class="comment">//上一层</span></span><br><span class="line">            List&lt;Integer&gt; list = triangle.get(i);</span><br><span class="line">            <span class="keyword">for</span> (<span class="keyword">int</span> j = <span class="number">0</span>; j &lt; list.size(); j ++) &#123;</span><br><span class="line">                <span class="keyword">int</span> a = list.get(j);<span class="comment">//当前的数字</span></span><br><span class="line">                <span class="keyword">int</span> upa = <span class="number">10000</span>;<span class="comment">//当前数字的上面</span></span><br><span class="line">                <span class="keyword">int</span> leftUpa = <span class="number">10000</span>;</span><br><span class="line">                <span class="keyword">if</span> (j &lt; preList.size())</span><br><span class="line">                    upa = preList.get(j);</span><br><span class="line">                <span class="keyword">if</span> (j &gt; <span class="number">0</span>)</span><br><span class="line">                    leftUpa = preList.get(j - <span class="number">1</span>);</span><br><span class="line">                </span><br><span class="line">                list.set(j,Math.min(a + upa, a + leftUpa));</span><br><span class="line">                <span class="comment">//set(int,e)</span></span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">int</span> min = <span class="number">10000</span>;</span><br><span class="line">        List&lt;Integer&gt; finalList = triangle.get(triangle.size() - <span class="number">1</span>);</span><br><span class="line">        <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; finalList.size(); i ++) &#123;</span><br><span class="line">            min = Math.min(finalList.get(i),min);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">return</span> min;</span><br><span class="line">    &#125;</span><br></pre></td></tr></table></figure>
<p>   也可以这样想，自底向上，最后到达的终点是(0,0)，这样最后直接输出(0,0)就行了。<br>   <figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">minimumTotal</span><span class="params">(List&lt;List&lt;Integer&gt;&gt; triangle)</span> </span>&#123;</span><br><span class="line">     <span class="keyword">for</span> (<span class="keyword">int</span> i = triangle.size() - <span class="number">2</span>; i &gt;= <span class="number">0</span>; i --) &#123;</span><br><span class="line">         List&lt;Integer&gt; downList = triangle.get(i + <span class="number">1</span>);<span class="comment">//下一层</span></span><br><span class="line">         List&lt;Integer&gt; list = triangle.get(i);</span><br><span class="line">         <span class="keyword">for</span> (<span class="keyword">int</span> j = <span class="number">0</span>; j &lt; list.size(); j ++) &#123;</span><br><span class="line">             <span class="keyword">int</span> a = list.get(j);<span class="comment">//当前的数字</span></span><br><span class="line">             <span class="keyword">int</span> downa = <span class="number">10000</span>;<span class="comment">//当前数字的上面</span></span><br><span class="line">             <span class="keyword">int</span> rightDowna = <span class="number">10000</span>;</span><br><span class="line">             <span class="comment">//if (j &lt; preList.size())//这一层的下一层一定会有</span></span><br><span class="line">                 downa = downList.get(j);</span><br><span class="line">             <span class="comment">//if (j &lt; list.size() - 1)</span></span><br><span class="line">                 rightDowna = downList.get(j + <span class="number">1</span>);</span><br><span class="line">             </span><br><span class="line">             list.set(j,Math.min(a + downa, a + rightDowna));</span><br><span class="line">             <span class="comment">//set(int,e)</span></span><br><span class="line">         &#125;</span><br><span class="line">     &#125;</span><br><span class="line">     <span class="comment">// int min = 10000;</span></span><br><span class="line">     <span class="comment">// List&lt;Integer&gt; finalList = triangle.get(triangle.size() - 1);</span></span><br><span class="line">     <span class="comment">// for (int i = 0; i &lt; finalList.size(); i ++) &#123;</span></span><br><span class="line">     <span class="comment">//     min = Math.min(finalList.get(i),min);</span></span><br><span class="line">     <span class="comment">// &#125;</span></span><br><span class="line">     <span class="keyword">return</span> triangle.get(<span class="number">0</span>).get(<span class="number">0</span>);</span><br><span class="line"> &#125;</span><br></pre></td></tr></table></figure><br> <strong>leetcode 71/100</strong></p>

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